Virtualisation is were you separate the computer, from the actual hardware it is running on. So your computer is exists virtually rather than actually.
You can install most PC operating systems onto a virtual machine (VM) in particular most Linux distributions or Windows or DOS. This can be useful on your own machine if you want to play around with another operating system without having a whole extra machine, i.e. run a Linux VM on your Windows computer, packages like VirtualBox exist that let you do this.
In a corporation this can be useful because most of your servers fully use their hardware resources, by letting them share hardware resources you get better utilisation of the hardware. So corporations build virtualisation stacks, computers with many many cores and large amounts of ram and disk space specifically to run virtualised servers. They will run virtualisation software such as VMWare.
A cloud is just a virtual environment run on someone elses computers providing computer resources as a service, i.e. AWS or MS Azure. You can rent a server from them. However a number of these cloud computing services have started making their software available so you can set-up you own cloud; if you do this behind a firewall or in an air-gaped environment then it is private so a private cloud.
A virtualisation stack and private cloud are more or less the same thing.